Proceedings Symposium IEEE/LEOS Benelux Chapter, 2003, Enschede
Burst bit-error rate calculation for GPON systems
B. Meerschman, Y. C. Yi, P. Ossieur, D. Verhulst, J. Bauwelinck, X. Z. Qiu, J. Vandewege
Ghent University, INTEC/IMEC, St.-Pietersnieuwstraat 41, B-9000 Gent,
Email: bart.meerschman@intec.ugent.be
This paper presents a methodology to calculate the bit-error rate for the data
transmission in the upstream direction of Gigabit PON systems. In traditional optical
receivers, the signal consists of a continuous bit stream. In the upstream direction of a
PON however, the signal consists of a succession of packets with varying amplitudes.
Hence the receiver needs to quickly extract the decision threshold and clock phase from
an overhead at the beginning of each packet. Such extraction results in a sensitivity
penalty. To estimate how big this penalty is as a function of system parameters, burst
bit-error rates need to be calculated.
Introduction
As an effective solution for broadband access, a lot of effort is made to develop PON
(Passive Optical Network) systems. Fig. 1 shows a schematic view of a typical PON
system. The Optical Line Termination (OLT), located in the Central Office, distributes
data towards the Optical Network Terminations (ONT’s), located at the user’s premises.
The end-user can also send data in the upstream direction towards the OLT. Note how
multiple users share the same transmission medium, giving rise to contention problems.
Hence, multiplexing is needed. An economical multiplexing technique in the upstream
direction is TDM (Time Division Multiplexing) in which each subscriber is allocated a
time slot to transmit data towards the OLT. As each ONT is located at different
distances from the OLT, this implies that the signal that needs to be handled by the
upstream receiver consists of a succession of packets with varying amplitude, see fig 2.
Upstream direction (1300 nm)
OLT
Passive splitter
ONT's
BMRx
Fiber feeder
Downstream direction (1550 nm)
Dedicated fiber
connections
Fig. 1 – Schematic view of a Passive Optical Network.
Recent developed ITU-T standards show an interest to increase the bit rate in PON’s
towards the Gbit/s region [1]. Such an increase in line rate can only be economical if
effort is spent to keep the number of subscribers as large as possible. This implies that
the receiver located in the OLT needs to have a low sensitivity and high dynamic range.
Combined with the GHz-bandwidth and packet-mode transmission, this creates several
challenges for the upstream receiver.
Indeed, to be able to handle the ITU-T G.984.1 data format [1], the upstream receiver
needs to be a dc-coupled burst-mode receiver. Such a receiver quickly extracts the
decision threshold during a short time (hereafter called the TDF – Threshold
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Burst bit-error rate calculation for GPON systems
Determination Field, see fig. 2) at the beginning of each packet. Furthermore, the
packets arrive at the receiver with an unknown clock phase (the clock frequency is
derived from the downstream transmission). Hence a circuit (CPA – Clock Phase
Alignment) follows the BMRx to quickly extract this phase, also from a short period
(hereafter called the CPA field) at the beginning of the packet. Furthermore, to bytealign the data payload, a delimiter is needed at the beginning of the packet.
1st packet
2nd packet
Overhead
TDF
CPA field
Overhead
Delimiter Data payload
Guard time
TDF
CPA field
Delimiter
Data payload
Fig. 2 – Upstream signal format (shown lengths do not correspond to real lengths).
While the ITU-T G.984.1 standard fixed the total length of the guard time and
overhead, no requirements are put on the assignment of bits to respectively guard time,
TDF, CPA field and delimiter. Hence the system designer should find an optimum
distribution of bits between these fields. For example, increasing the TDF length can
improve the sensitivity of the BMRx, but may reduce the performance of the CPA unit
as it has fewer bits available to extract the correct clock phase. A detailed study of burst
bit-error rates (BBERs), the subject of this paper, is needed to find an optimum.
To calculate the BBER, the problem is divided into two parts. First, the BBER is
calculated after the amplitude recovery done by the BMRx. Then, using a distribution of
the sampling moment obtained by the CPA circuit, the final BBER can be calculated for
various settings of the system parameters.
The burst bit-error rate after the BMRx
There exists a large amount of literature on how to calculate the BER for traditional
optical receivers [2]. The developed methods can be adapted to calculate the BBER for
burst-mode transmission. To correctly evaluate the BBER for GPON applications, at
least three points need to be included in the BMRx model. First of all, as an avalanche
photodiode (APD) is used in the BMRx, a detailed model of the avalanche
multiplication noise needs to be included. Secondly, note that the BMRx extracts the
decision threshold with a small time constant. This implies that this threshold can no
longer be treated as a fixed level, but instead shows a certain statistical distribution [3].
This gives rise to a sensitivity penalty. Last of all, as the BMRx is fully dc-coupled the
model should include the influence of dc-offsets on the sensitivity.
In [4], a model was presented that can take into account the mentioned effects. Using
an N-points non-classical Gaussian Quadrature Rule, the BER can be calculated for
given system parameters. It is shown that the influence of DC-offsets can be the
dominating effect in reducing the sensitivity of a BMRx when compared to a traditional
receiver, with the same system parameters (such as avalanche gain, transimpedance gain,
thermal receiver noise etc.).
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Proceedings Symposium IEEE/LEOS Benelux Chapter, 2003, Enschede
The burst bit-error rate after the CPA
The CPA unit recovers timing information based on a digital input signal coming
from the BMRx. The CPA determines a sample moment based on the CPA of the burst
preamble, which consists of a ‘01’ sequence. The CPA will try to measure the middle of
an isolated ‘1’ bit, and use those measurement results to determine a sample moment ts.
The digital input signal is characterized by the jitter ei on the rising and falling edges,
defined as the difference between the time ti’ that a transition is expected to occur and
the time ti that the transition actually occurs. It is divided into two categories:
deterministic jitter (DJ) and random jitter (RJ). RJ is considered an unbounded
component, described using a Gaussian distribution with mean 0 and standard deviation
σjitter. DJ is considered bounded, and is composed of intersymbol interference, duty
cycle distortion and period jitter components.
Once the input jitter characteristics are known the probability density function (PDF)
of the ts only depends on the length of the CPA field and how accurate the CPA unit can
measure a sample moment. In fig. 3a and 3b the PDF of ts is plotted for several lengths
of the CPA field when the sample accuracy of the CPA unit is one tenth of the bit
period. Fig. 3c-d shows the PDF of t s for several CPA accuracies with a fixed CPA field
length of 22 bits.
1
0.5
0.1
0.01
1 .10
Prob ( t , 20)
0.01
Pr[ t, NoB]
Pr[ t, NoB]
Prob ( t , 20)
Prob ( t , 16)
Prob ( t , 8)
Prob ( t , 2)
Prob ( t , 16)
3
4
1 .10
1 .10
5
.
Prob ( t , 2) 1 10
6
1 .10
7
1 .10
8
Prob ( t , 8)
0.005
9
1 .10
10
0
0
100
200
300
400
500
600
700
− 10
1 .10
800
10
0
100
200
0
t
Sample instant t [ps]
300
400
500
600
700
800
t
Sample instant t [ps]
(a)
T
(b)
0.015
1
0.5
0.1
Prob ( t , 400)
0.01
Pr[ t, accuracy]
Pr[ t, accuracy]
0.01
Prob ( t , 200)
Prob ( t , 100)
Prob ( t , 80)
1 .10
3
1 .10
4
1 .10
5
.
Prob( t , 80) 1 10
6
Prob( t , 400)
Prob( t , 200)
Prob( t , 100)
0.005
7
1 .10
1 .10
1 .10
− 10
− 10
10
10
0
0
100
200
300
400
500
t
Sample instant t [ps]
600
700
1 .10
8
9
10
0
800
T
(c)
0
100
200
300
400
500
600
700
800
t
Sample instant t [ps]
(d)
Fig. 3 PDF of sample instant t plotted in linear and logarithmic scale for several lengths of the CPA
field (NoB – No of Bits) and CPA accuracies (accuracy). σjitter = 50 ps, bit period T = 800 ps
(a-b) CPA accuracy = 80 ps (c-d) CPA field length = 22
Based on the bathtub plot and the above distribution the total BBER can be calculated as
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T
Burst bit-error rate calculation for GPON systems
BBER =
∫ BBER(t
T
0
[
sample ). Pr t sample
].dt sample
(1)
The delimiter field
The delimiter is a unique pattern indicating the start of the burst, which can be used
to perform byte synchronization. The delimiter must provide sufficient data bits to
perform a robust delimiter function in the face of bit errors. The two possible problems
are either the detection of a nonexistent header or the inability to detect the header due
to the presence of errors.
To protect the delimiter it must be constructed in such a way that the shifted version
of itself over all preamble bits has a maximum hamming distance d. It can be
empirically verified [1] that for all the delimiters of sizes ranging from 8 to 20 bits this
maximum hamming distance d equals int(N/2) –1, where N is the number of bits in the
delimiter. Then the delimiter recognition unit will be able to handle t errors, where t is
the error correcting capability of the code and is equal to int(N/4)-1.
The probability of failure to detect the delimiter is approximated by the formula [1]:
N


 BBER int( N / 4)
Pseb = 
 int( N / 4) 
(2)
where BBER is the burst bit error rate of the CPA output signal. In order to suppress this
kind of error Pseb should be less then 10-10 for all BBER smaller then 10-4. This
constraint results in a delimiter length of at least 16 bits.
Conclusion and future work
It has been shown how burst bit-error rates can be calculated for GPON’s and how to
take into account the properties of the burst-mode receiver chain. These calculations
will be used to determine an optimum distribution of the TDF, CPA and delimiter field
lengths.
Acknowledgement
This work is funded by the European IST (Information Society Technologies) project
GIANT for supporting this research. The authors wish to thank their GIANT partners of
the National Technical University Athens and Paolo Solina of Telecom Italia Lab for
their cooperation. Bart Meerschman is in debt to the Flemish IWT for his research
fellowship and for financial support.
References
[1] ITU-T G.984.1 Recommendation: “Gigabit-capable Passive Optical Networks (GPON): Physical
Media Dependent (PMD) layer Specification”.
[2] R. Dogliotti, A. Luvison, G. Pirani, “Error probability in optical fiber transmission systems”, IEEE
Trans. Inform. Theory, vol. IT-25, pp. 170-179, March 1979.
[3] C. A. Eldering, “Theoretical determination of sensitivity penalty for burst mode fiber optic
receivers”, J. Lightwave Technol. vol. 11, pp. 2145-2149, Dec. 1993.
[4] P. Ossieur, Xing-Zhi Qiu, Johan Bauwelinck and Jan Vandewege, "Sensitivity penalty calculation for
burst-mode receivers using avalanche photodiodes", to be published in J. Lightwave Technol., Nov
2003, Special Issue on Optical Networking.
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